Stability analysis for fractional‐order neural networks with time‐varying delay

Wang, Fengxian; Zhang, Jie; Shu, Yan-Jun; Liu, Xinge

doi:10.1002/asjc.2944

Cited by 6 publications

(3 citation statements)

References 40 publications

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“…The simulated state trajectories x(𝜍) and steering control function u(𝜍) are shown in Figures 1 and 2, respectively. From the Figure 1, we observe that the state (13) of the system (12) is starts from the initial state…”

Section: Numerical Examplesmentioning

confidence: 99%

“…When comparing fractional order derivative to integer order derivative, it is possible to capture memory effects in the systems. Using fractional derivative, there are plenty of articles found in control theory [8][9][10][11][12]. In general, fractional dynamical systems with delays in the control or the state have more trouble for performing.…”

Section: Introductionmentioning

confidence: 99%

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Controllability of fractional dynamical systems with distributed delays in control using ψ‐Caputo fractional derivative

Selvam¹,

Govindaraj²

2023

Asian Journal of Control

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This research investigates the controllability of linear and non‐linear fractional dynamical systems with distributed delays in control using the ‐Caputo fractional derivative. For controllability of linear systems, the positive definiteness of Grammian matrix, which is characterized by Mittag–Leffler functions, is used to provide necessary and sufficient conditions. For the controllability of non‐linear systems, the iterative technique with the completeness of is used to obtain sufficient conditions. Using the ‐Caputo fractional derivative, this study is new since it investigates the ideas of controllability. A couple of numerical results are offered to explain the theoretical results.

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Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Controllability of fractional dynamical systems with distributed delays in control using ψ‐Caputo fractional derivative

Selvam¹,

Govindaraj²

2023

Asian Journal of Control

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“…Compressed sensing does not apply to some non-sparse networks, and the sparse representation of the signals must be incoherent, which is not straightforward to achieve in real networks. Along with the development of modern control theorems, the TICDN problem based on synchronization methods has gradually attracted the attention of researchers in recent years, This method has been explained in detail and proven rigorously via the Lyapunov stability theory [ 26 ], Linear Matrix Inequalities (LMI) [ 27 ], and many other techniques [ 28 , 29 ]. Unknown topology can be identified via the proposed STO, and the response–drive networks have to actualize synchronization.…”

Section: Introductionmentioning

confidence: 99%

Design of a Robust Synchronization-Based Topology Observer for Complex Delayed Networks with Fixed and Adaptive Coupling Strength

Sun,

Wu,

Chen

et al. 2024

Entropy

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Network topology plays a key role in determining the characteristics and dynamical behaviors of a network. But in practice, network topology is sometimes hidden or uncertain ahead of time because of network complexity. In this paper, a robust-synchronization-based topology observer (STO) is proposed and applied to solve the problem of identifying the topology of complex delayed networks (TICDNs). In comparison to the existing literature, the proposed STO does not require any prior knowledge about the range of topological parameters and does not have strict limits on topology type. Furthermore, the proposed STO is suitable not only for networks with fixed coupling strength, but also for networks with adaptive coupling strength. Finally, a few comparison examples for TICDNs are used to verify the feasibility and efficiency of the proposed STO, and the results show that the proposed STO outperforms the other methods.

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Controllability, observability, and stability of φ‐conformable fractional linear dynamical systems

Sadek

2024

Asian Journal of Control

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This paper focuses on two main aspects. Firstly, we introduce a generalized form of conformable fractional derivatives called ‐conformable fractional derivatives along with their corresponding integrals . We also present several theorems related to these derivatives. Secondly, we investigate the observability, controllability, and stability of a fractional dynamical system known as the ‐conformable fractional dynamical system ( ‐CF‐DS). We establish the connection between controllability, the controllability matrix, and the fractional ‐conformable fractional differential Lyapunov equation ( ‐CF‐DLE). We prove that the ‐CF‐DS is stable if and only if all eigenvalues of the matrix have negative real parts. Moreover, we provide theorems regarding the observability of an ‐CF‐DS. To demonstrate the efficacy of our results, we include illustrative examples.

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Stability analysis for fractional‐order neural networks with time‐varying delay

Cited by 6 publications

References 40 publications

Controllability of fractional dynamical systems with distributed delays in control using ψ‐Caputo fractional derivative

Controllability of fractional dynamical systems with distributed delays in control using ψ‐Caputo fractional derivative

Design of a Robust Synchronization-Based Topology Observer for Complex Delayed Networks with Fixed and Adaptive Coupling Strength

Controllability, observability, and stability of φ‐conformable fractional linear dynamical systems

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